Q23 of 47 Page 1

If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9th terms.

Let the 'a' and 'A' be the first term of two AP's


And 'd' and 'D' be the common difference of the AP with first term as 'a' and 'A' respectively.


Also, let their nth term be an and An and sum of nth terms be sn and Sn.


We know, that sum of first n terms of an an AP is



Where, a is first term and d is common difference


Given,




Put n = 2(9) - 1 = 17


[we choose, n = 2m - 1 for calculating ratio of mth terms]






Hence, ratio of 9th terms is 24:19


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